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S-DUALITY
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The second big duality that has been discovered is S-duality. Remember that a coupling constant determines the strength of an interaction, and in string theory the dilaton eld determines the value of the coupling constant. String theories have different coupling constants that are weak or strong. By letting where is the dilaton eld, since the coupling constant is de ned from g = exp , we see that we can transform a large coupling constant into a small one and vice versa, changing a strong interaction into a weak one and vice versa. This is what S-duality is about. S-duality brings type I superstring theory into the fold. That is, under S-duality Type I superstring theory is related to heterotic SO(32) superstring theory. Type II B is S-dual to itself. So, a strong interaction in Type I superstring theory is the same as a weak interaction in heterotic SO(32) theory, and vice versa. In other words, the two theories are really the same theory at different coupling strengths.
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1. T-duality relates string theories in which way (a) It relates strong interactions in type II A theory to weak interactions in type II B theory. (b) It relates strong interactions in heterotic theory to weak interactions in type I theory. (c) It relates large and small distance scales and momentum and winding modes in two different theories. (d) It only relates large and small distance scales. 2. The most signi cant difference between superstring theory and bosonic theory is (a) Bosonic theory has 16 extra space-time dimensions. (b) Superstring theory eliminates tachyon states and incorporates fermions into the theory.
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String Theory Demysti ed
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(c) Bosonic string theory eliminates tachyons. (d) Superstring theory has an unstable vacuum.
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3. The difference between types II A and type II B theory is (a) Type II A theory is nonchiral and type II B theory is chiral. (b) Type II A theory only describes open strings. (c) Type II B theory only describes bosons. (d) Type II B theory is nonchiral and type II A theory is chiral. 4. The dilaton eld (a) Is only found in bosonic string theory. (b) Is related to the coupling constant, but only in heterotic theory. (c) Is related to the coupling constant in all string theories. (d) Is known to be a mathematical trick not found in nature. 5. Physicists were excited by dualities because (a) They add fermions to the theory. (b) They show that the ve superstring theories are related, so are different aspects of an underlying, unknown theory. (c) They show that bosonic and superstring theories are related, so are different aspects of an underlying, unknown theory. 6. The number of space-time dimensions in string theory (a) Is xed at 26 by an ad hoc assumption. (b) Is xed at 26 for superstring theories and 10 for bosonic string theory, because this eliminates ghost states from the theory. (c) Is xed at 10 for superstring theories and 26 for bosonic string theory, because this eliminates tachyon states from the theory. (d) Is xed at 10 for superstring theories and 26 for bosonic string theory, because this eliminates ghost states from the theory.
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In this chapter, we will review the states of type II A and type II B superstrings. We will do so using the worldsheet supersymmetry plus Gliozzi-Scherk-Olive (GSO) projection approach because it s a bit simpler, so we will review some of the discussion of Chap. 7. In the next chapter, we will brie y discuss heterotic superstrings.
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The R and NS Sectors
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To introduce worldsheet supersymmetry we began with the action [Eq. (7.2)]: S= T 2 d ( X X i ) 2
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String Theory Demysti ed
In the light-cone gauge, the fermionic part of the action assumes the form SF = iT d 2 ( + + + + ) In type II string theories, we only consider closed strings. Therefore, we apply periodic boundary conditions. There are actually two possibilities. Periodic boundary conditions are known as Ramond (R) boundary conditions:
A ( ) = A ( + 2 )
(11.1)
Antiperiodic boundary conditions are called Neveu-Schwarz (NS):
A ( ) = A ( + 2 )
(11.2)
Remember that a closed string has independent left-moving and right-moving modes. We can apply either periodic or antiperiodic boundary conditions to the leftand right-moving modes independently, which will give us four possibilities, as discussed in Chap. 7.
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